/*=========================================================================
 *
 *  Copyright Insight Software Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *         http://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
#ifndef itkAffineTransform_h
#define itkAffineTransform_h

#include "itkMatrixOffsetTransformBase.h"
#include <iostream>


namespace itk
{
/**
 * Affine transformation of a vector space (e.g. space coordinates)
 *
 * This class allows the definition and manipulation of affine
 * transformations of an n-dimensional affine space (and its
 * associated vector space) onto itself.  One common use is to define
 * and manipulate Euclidean coordinate transformations in two and
 * three dimensions, but other uses are possible as well.
 *
 * An affine transformation is defined mathematically as a linear
 * transformation plus a constant offset.  If A is a constant n x n
 * matrix and b is a constant n-vector, then y = Ax+b defines an
 * affine transformation from the n-vector x to the n-vector y.
 *
 * The difference between two points is a vector and transforms
 * linearly, using the matrix only.  That is, (y1-y2) = A*(x1-x2).
 *
 * The AffineTransform class determines whether to transform an object
 * as a point or a vector by examining its type.  An object of type
 * Point transforms as a point; an object of type Vector transforms as
 * a vector.
 *
 * One common use of affine transformations is to define coordinate
 * conversions in two- and three-dimensional space.  In this
 * application, x is a two- or three-dimensional vector containing the
 * "source" coordinates of a point, y is a vector containing the
 * "target" coordinates, the matrix A defines the scaling and rotation
 * of the coordinate systems from the source to the target, and b
 * defines the translation of the origin from the source to the
 * target.  More generally, A can also define anisotropic scaling and
 * shearing transformations.  Any good textbook on computer graphics
 * will discuss coordinate transformations in more detail.  Several of
 * the methods in this class are designed for this purpose and use the
 * language appropriate to coordinate conversions.
 *
 * Any two affine transformations may be composed and the result is
 * another affine transformation.  However, the order is important.
 * Given two affine transformations T1 and T2, we will say that
 * "precomposing T1 with T2" yields the transformation which applies
 * T1 to the source, and then applies T2 to that result to obtain the
 * target.  Conversely, we will say that "postcomposing T1 with T2"
 * yields the transformation which applies T2 to the source, and then
 * applies T1 to that result to obtain the target.  (Whether T1 or T2
 * comes first lexicographically depends on whether you choose to
 * write mappings from right-to-left or vice versa; we avoid the whole
 * problem by referring to the order of application rather than the
 * textual order.)
 *
 * There are two template parameters for this class:
 *
 * ScalarT       The type to be used for scalar numeric values.  Either
 *               float or double.
 *
 * NDimensions   The number of dimensions of the vector space.
 *
 * This class provides several methods for setting the matrix and vector
 * defining the transform. To support the registration framework, the
 * transform parameters can also be set as an Array<double> of size
 * (NDimension + 1) * NDimension using method SetParameters().
 * The first (NDimension x NDimension) parameters defines the matrix in
 * row-major order (where the column index varies the fastest).
 * The last NDimension parameters defines the translation
 * in each dimensions.
 *
 * This class also supports the specification of a center of rotation (center)
 * and a translation that is applied with respect to that centered rotation.
 * By default the center of rotation is set to the origin.
 *
 * \ingroup ITKTransform
 */

template<
  typename TParametersValueType = double,
  unsigned int NDimensions = 3 >
// Number of dimensions in the input space
class AffineTransform:
  public MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions>
{
public:
  /** Standard typedefs   */
  typedef AffineTransform Self;
  typedef MatrixOffsetTransformBase< TParametersValueType,
                                     NDimensions,
                                     NDimensions >  Superclass;

  typedef SmartPointer<Self>       Pointer;
  typedef SmartPointer<const Self> ConstPointer;

  /** Run-time type information (and related methods).   */
  itkTypeMacro(AffineTransform, MatrixOffsetTransformBase);

  /** New macro for creation of through a Smart Pointer   */
  itkNewMacro(Self);

  /** Dimension of the domain space. */
  itkStaticConstMacro(InputSpaceDimension, unsigned int, NDimensions);
  itkStaticConstMacro(OutputSpaceDimension, unsigned int, NDimensions);
  itkStaticConstMacro(SpaceDimension, unsigned int, NDimensions);
  itkStaticConstMacro( ParametersDimension, unsigned int,
                       NDimensions *( NDimensions + 1 ) );

  /** Parameters Type   */
  typedef typename Superclass::ParametersType            ParametersType;
  typedef typename Superclass::FixedParametersType       FixedParametersType;
  typedef typename Superclass::JacobianType              JacobianType;
  typedef typename Superclass::ScalarType                ScalarType;
  typedef typename Superclass::InputPointType            InputPointType;
  typedef typename Superclass::OutputPointType           OutputPointType;
  typedef typename Superclass::InputVectorType           InputVectorType;
  typedef typename Superclass::OutputVectorType          OutputVectorType;
  typedef typename Superclass::InputVnlVectorType        InputVnlVectorType;
  typedef typename Superclass::OutputVnlVectorType       OutputVnlVectorType;
  typedef typename Superclass::InputCovariantVectorType  InputCovariantVectorType;
  typedef typename Superclass::OutputCovariantVectorType OutputCovariantVectorType;
  typedef typename Superclass::MatrixType                MatrixType;
  typedef typename Superclass::InverseMatrixType         InverseMatrixType;
  typedef typename Superclass::CenterType                CenterType;
  typedef typename Superclass::OffsetType                OffsetType;
  typedef typename Superclass::TranslationType           TranslationType;

  /** Base inverse transform type. This type should not be changed to the
   * concrete inverse transform type or inheritance would be lost.*/
  typedef typename Superclass::InverseTransformBaseType InverseTransformBaseType;
  typedef typename InverseTransformBaseType::Pointer    InverseTransformBasePointer;

  /** Compose affine transformation with a translation
   *
   * This method modifies self to include a translation of the
   * origin.  The translation is precomposed with self if pre is
   * true, and postcomposed otherwise.
   * This updates Translation based on current center. */
  void Translate(const OutputVectorType & offset, bool pre = 0);

  /** Compose affine transformation with a scaling
   *
   * This method modifies self to magnify the source by a given
   * factor along each axis.  If all factors are the same, or only a
   * single factor is given, then the scaling is isotropic;
   * otherwise it is anisotropic.  If an odd number of factors are
   * negative, then the parity of the image changes.  If any of the
   * factors is zero, then the transformation becomes a projection
   * and is not invertible.  The scaling is precomposed with self if
   * pre is true, and postcomposed otherwise.
   * Note that the scaling is applied centered at the origin. */
  void Scale(const OutputVectorType & factor, bool pre = 0);

  void Scale(const TParametersValueType & factor, bool pre = 0);

  /** Compose affine transformation with an elementary rotation
   *
   * This method composes self with a rotation that affects two
   * specified axes, replacing the current value of self.  The
   * rotation angle is in radians.  The axis of rotation goes
   * through the origin.  The transformation is given by
   *
   * y[axis1] =  std::cos(angle)*x[axis1] + std::sin(angle)*x[axis2]
   * y[axis2] = -sin(angle)*x[axis1] + std::cos(angle)*x[axis2].
   *
   * All coordinates other than axis1 and axis2 are unchanged;
   * a rotation of pi/2 radians will carry +axis1 into +axis2.
   * The rotation is precomposed with self if pre is true, and
   * postcomposed otherwise.
   * Note that the rotation is applied centered at the origin. */
  void Rotate(int axis1, int axis2, TParametersValueType angle, bool pre = 0);

  /** Compose 2D affine transformation with a rotation
   *
   * This method composes self, which must be a 2D affine
   * transformation, with a clockwise rotation through a given angle
   * in radians.  The center of rotation is the origin.  The
   * rotation is precomposed with self if pre is true, and
   * postcomposed otherwise.
   * Note that the rotation is applied centered at the origin.
   *
   * \warning Only to be use in two dimensions
   *
   * \todo Find a way to generate a compile-time error
   *       is this is used with NDimensions != 2. */
  void Rotate2D(TParametersValueType angle, bool pre = 0);

  /** Compose 3D affine transformation with a rotation
   *
   * This method composes self, which must be a 3D affine
   * transformation, with a clockwise rotation around a specified
   * axis.  The rotation angle is in radians; the axis of rotation
   * goes through the origin.  The rotation is precomposed with self
   * if pre is true, and postcomposed otherwise.
   * Note that the rotation is applied centered at the origin.
   *
   * \warning Only to be used in dimension 3
   *
   * \todo Find a way to generate a compile-time error
   * is this is used with NDimensions != 3. */
  void Rotate3D(const OutputVectorType & axis, TParametersValueType angle, bool pre = 0);

  /** Compose affine transformation with a shear
   *
   * This method composes self with a shear transformation,
   * replacing the original contents of self.  The shear is
   * precomposed with self if pre is true, and postcomposed
   * otherwise.  The transformation is given by
   *
   * y[axis1] = x[axis1] + coef*x[axis2]
   * y[axis2] =                 x[axis2].
   *
   * Note that the shear is applied centered at the origin. */
  void Shear(int axis1, int axis2, TParametersValueType coef, bool pre = 0);

  /** Get an inverse of this transform. */
  bool GetInverse(Self *inverse) const;

  /** Return an inverse of this transform. */
  virtual InverseTransformBasePointer GetInverseTransform() const ITK_OVERRIDE;

  /** Back transform by an affine transformation
   *
   * This method finds the point or vector that maps to a given
   * point or vector under the affine transformation defined by
   * self.  If no such point exists, an exception is thrown.
   *
   * \deprecated Please use GetInverseTransform and then call the
   *   forward transform function */
  itkLegacyMacro(InputPointType   BackTransform(const OutputPointType  & point) const);
  itkLegacyMacro(InputVectorType  BackTransform(const OutputVectorType & vector) const);
  itkLegacyMacro(InputVnlVectorType BackTransform( const OutputVnlVectorType & vector) const);
  itkLegacyMacro(InputCovariantVectorType BackTransform( const OutputCovariantVectorType & vector) const);

  /** Back transform a point by an affine transform
   *
   * This method finds the point that maps to a given point under
   * the affine transformation defined by self.  If no such point
   * exists, an exception is thrown.  The returned value is (a
   * pointer to) a brand new point created with new.
   *
   * \deprecated Please use GetInverseTransform and then call the
   *   forward transform function */
  itkLegacyMacro(InputPointType BackTransformPoint(const OutputPointType  & point) const);

  /** Compute distance between two affine transformations
   *
   * This method computes a ``distance'' between two affine
   * transformations.  This distance is guaranteed to be a metric,
   * but not any particular metric.  (At the moment, the algorithm
   * is to collect all the elements of the matrix and offset into a
   * vector, and compute the euclidean (L2) norm of that vector.
   * Some metric which could be used to estimate the distance between
   * two points transformed by the affine transformation would be
   * more useful, but I don't have time right now to work out the
   * mathematical details.) */
  ScalarType Metric(const Self *other) const;

  /** This method computes the distance from self to the identity
   * transformation, using the same metric as the one-argument form
   * of the Metric() method. */
  ScalarType Metric() const;

protected:
  /** Construct an AffineTransform object
   *
   * This method constructs a new AffineTransform object and
   * initializes the matrix and offset parts of the transformation
   * to values specified by the caller.  If the arguments are
   * omitted, then the AffineTransform is initialized to an identity
   * transformation in the appropriate number of dimensions.   */
  AffineTransform(const MatrixType & matrix,
                  const OutputVectorType & offset);
  AffineTransform(unsigned int paramDims);
  AffineTransform();

  /** Destroy an AffineTransform object   */
  virtual ~AffineTransform();

  /** Print contents of an AffineTransform */
  void PrintSelf(std::ostream & s, Indent indent) const ITK_OVERRIDE;

private:

  AffineTransform(const Self & other);
  const Self & operator=(const Self &);
}; //class AffineTransform

#if !defined(ITK_LEGACY_REMOVE)
/** Back transform a vector */
template<typename TParametersValueType, unsigned int NDimensions>
inline
typename AffineTransform<TParametersValueType, NDimensions>::InputVectorType
AffineTransform<TParametersValueType, NDimensions>::BackTransform(const OutputVectorType & vect) const
{
  itkWarningMacro(
    << "BackTransform(): This method is slated to be removed "
    << "from ITK. Instead, please use GetInverse() to generate an inverse "
    << "transform and then perform the transform using that inverted transform.");
  return this->GetInverseMatrix() * vect;
}

/** Back transform a vnl_vector */
template<typename TParametersValueType, unsigned int NDimensions>
inline
typename AffineTransform<TParametersValueType, NDimensions>::InputVnlVectorType
AffineTransform<TParametersValueType, NDimensions>::BackTransform(const OutputVnlVectorType & vect) const
{
  itkWarningMacro(
    << "BackTransform(): This method is slated to be removed "
    << "from ITK. Instead, please use GetInverse() to generate an inverse "
    << "transform and then perform the transform using that inverted transform.");
  return this->GetInverseMatrix() * vect;
}

/** Back Transform a CovariantVector */
template<typename TParametersValueType, unsigned int NDimensions>
inline
typename AffineTransform<TParametersValueType, NDimensions>::InputCovariantVectorType
AffineTransform<TParametersValueType, NDimensions>::BackTransform(const OutputCovariantVectorType & vec) const
{
  itkWarningMacro(
    << "BackTransform(): This method is slated to be removed "
    << "from ITK. Instead, please use GetInverse() to generate an inverse "
    << "transform and then perform the transform using that inverted transform.");

  InputCovariantVectorType result;    // Converted vector

  for ( unsigned int i = 0; i < NDimensions; i++ )
    {
    result[i] = NumericTraits< ScalarType >::ZeroValue();
    for ( unsigned int j = 0; j < NDimensions; j++ )
      {
      result[i] += this->GetMatrix()[j][i] * vec[j]; // Direct matrix transposed
      }
    }
  return result;
}

/** Back transform a given point which is represented as type PointType */
template<typename TParametersValueType, unsigned int NDimensions>
inline
typename AffineTransform<TParametersValueType, NDimensions>::InputPointType
AffineTransform<TParametersValueType, NDimensions>::BackTransformPoint(const OutputPointType & point) const
{
  return this->BackTransform(point);
}

/** Back transform a point */
template<typename TParametersValueType, unsigned int NDimensions>
inline
typename AffineTransform<TParametersValueType, NDimensions>::InputPointType
AffineTransform<TParametersValueType, NDimensions>::BackTransform(const OutputPointType & point) const
{
  itkWarningMacro(
    << "BackTransform(): This method is slated to be removed "
    << "from ITK.  Instead, please use GetInverse() to generate an inverse "
    << "transform and then perform the transform using that inverted transform.");
  InputPointType result;       // Converted point
  ScalarType     temp[NDimensions];
  unsigned int   i, j;

  for ( j = 0; j < NDimensions; j++ )
    {
    temp[j] = point[j] - this->GetOffset()[j];
    }

  for ( i = 0; i < NDimensions; i++ )
    {
    result[i] = 0.0;
    for ( j = 0; j < NDimensions; j++ )
      {
      result[i] += this->GetInverseMatrix()[i][j] * temp[j];
      }
    }
  return result;
}
#endif
}  // namespace itk

#ifndef ITK_MANUAL_INSTANTIATION
#include "itkAffineTransform.hxx"
#endif

#endif /* itkAffineTransform_h */
